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Difficulty: MediumCircular Motion and Centripetal Force

An automotive engineer is analyzing the physics of a racecar driving along a flat, circular test track. Match each observed physical phenomenon during the turn with its correct mechanical explanation.

  • The required force that allows the car to successfully navigate the curve.An inward centripetal force provided by the friction of the tires.
  • The driver's sensation of being pressed outward against the side door.The body's natural inertia resisting the car's continuous change in direction.
  • The vehicle's trajectory if it suddenly hits a patch of completely frictionless ice.Movement in a straight line tangent to the edge of the circular path.
  • The change in required tire grip if the car navigates the same curve at twice the speed.The necessary inward force increases by a factor of four.

Answer

The turning force is an inward centripetal force provided by friction. The outward sensation is caused by inertia. Losing friction results in a tangential straight-line path, and doubling the speed quadruples the required centripetal force.
Each matching pair accurately connects real-world driving observations with Newton's laws of motion. Circular paths require inward centripetal forces. Physical sensations of being pushed outward are simply inertia. Loss of that inward force results in a straight, tangential trajectory, and the mathematical relationship of F=mv2rF = \frac{mv^2}{r} dictates that doubling speed requires four times the inward force.

Step-by-Step Solution

1
Identify the primary force enabling circular motion.
The car requires a net inward force, known as centripetal force, which is supplied by road friction.
Without a force pulling the object toward the center of the curve, circular motion is impossible.
2
Analyze the physical cause of the driver's outward sensation.
The sensation is determined to be the result of inertia, not a real physical outward force.
Newton's First Law states objects resist changes in direction. The body tries to go straight while the car door pushes inward.
3
Determine the path of the vehicle if the centripetal force drops to zero (hitting ice).
The path becomes a straight line tangent to the exact point on the curve where friction was lost.
When the inward force ceases, the vehicle instantly resumes straight-line motion.
4
Calculate the proportional change in force if velocity is doubled.
Using F=mv2rF = \frac{mv^2}{r}, inserting 2v2v yields (2v)2=4v2(2v)^2 = 4v^2, meaning the required force is 4 times greater.
Centripetal force scales with the square of the velocity.

Key Concept

Centripetal Force, Inertia, and Tangential Velocity in Circular Motion
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Topics

Circular Motion and Centripetal Force

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